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arXiv:quant-ph/0302094 · Physical Review A

Enhanced thermal entanglement in an anisotropic HeisenbergXYZchain

Ling Zhou, H. S. Song, Yanqing Guo, Changchun Li

Published Aug 6, 2003• 214 citations
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Abstract

The thermal entanglement in the Heisenberg $\mathrm{XYZ}$ chain is investigated in the presence of an external magnetic field B. In the two-qubit system, the critical magnetic field ${B}_{c}$ is increased by introducing the interaction of the z component of two neighboring spins ${J}_{z}.$ This interaction not only improves the critical temperature ${T}_{c},$ but also enhances the entanglement for a particular fixed B. We also analyze the pairwise entanglement between nearest neighbors in three qubits. The pairwise entanglement, for a fixed T, can become strong by controlling B and ${J}_{z}.$

DOI
10.1103/physreva.68.024301

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The thermal entanglement in the Heisenberg XYZ\mathrm{XYZ}XYZ chain is investigated in the presence of an external magnetic field B. In the two-qubit system, the critical magnetic field Bc{B}_{c}Bc​ is increased by introducing the interaction of the z component of two neighboring spins Jz.{J}_{z}.Jz​. This interaction not only improves the critical temperature Tc,{T}_{c},Tc​, but also enhances the entanglement for a particular fixed B. We also analyze the pairwise entanglement between nearest neighbors in three qubits. The pairwise entanglement, for a fixed T, can become strong by controlling B and Jz.{J}_{z}.Jz​.
The thermal entanglement in a two-qubit Heisenberg XXZXXZXXZ spin chain is investigated under an inhomogeneous magnetic field bbb. We show that the ground-state entanglement is independent of the interaction of zzz-component Jz{J}_{z}Jz​. The thermal entanglement at the fixed temperature can be enhanced when Jz{J}_{z}Jz​ increases. We strictly show that for any temperature TTT and Jz{J}_{z}Jz​, the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field bc{b}_{c}bc​ is independent of Jz{J}_{z}Jz​. The critical magnetic field Bc{B}_{c}Bc​ increases with the increasing $\ensuremath{\mid}b\ensuremath{\mid}$ but the maximum entanglement value that the system can arrive at becomes smaller.
We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.
In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.
We investigate the entanglement of a two-qubit anisotropic Heisenberg XY chain in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z axis. By means of the combined influences of anisotropic interactions and a magnetic field B, one is able to produce entanglement for any finite T, by adjusting the magnetic field strength. This contrasts with the isotropic interaction or the B = 0 cases, for which there is no entanglement above a critical temperature T(c) that is independent of the external B field.
The pair-wise thermal entanglement in a four-qubit Heisenberg XXZ chain is investigated to study the role of anisotropy when an external magnetic field is included. It is found that pair-wise entanglement is absent between nearest- and next-nearest neighbouring qubits with anisotropic parameter Δ⩽−1. For two nearest-neighbouring qubits, increasing the parameter can not only induce the entanglement, but also extend the entanglement region in terms of magnetic field B and temperature T . For two next-nearest-neighbouring qubits, increasing anisotropic parameter can shift the location of the entanglement and control the extent of the entanglement in terms of magnetic field at a finite temperature.
Thermal pairwise entanglement of a three-qubit Heisenberg XX chain with the Dzyaloshinski-Moriya(DM) anisotropic antisymmetric interaction under an external magnetic field and quantum teleportation when using the Heisenberg chain as a channel are investigated.The entanglement and fidelity depending on the DM interaction,magnetic field and temperature are given in detail.The results show that the thermal entanglement can be controlled by magnetic field and DM interaction.Quantum teleportation will be better realized via an ferromagnetic spinchain when the DM interaction and external magnetic field are turned off and the temperature is low.The thermal entanglement cannot completely reflect the teleportation fidelity,and the same thermal entanglement could yield different average teleportation fidelities.